An ab initio study of model compounds of fecapentaenes

Journal of Molecular Structure (Theo&m), 167 (1988) 359-394 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

AN AB INITIO STUDY OF MODEL COMPOUNDS FECAPENTAENES

359

OF

JOHN FRANK MARCOCCIA, IMRE G. CSIZMADIA and PETER YATES Department of Chemistry, University of Toronto, Toronto, Ontario M5S 1Al (Canada) JIRI J. KREPINSKY DepartmentsofMedicalBiophysics M5S 1Al (Canada)

andMedicalGenetics,

Universityof Toronto, Toronto, Ontario

(Received 19 August 1987)

ABSTRACT Total geometry optimixations at the STO-3G and 3-21G basis levels, as well as single point energy determinations using the 6-31G* basis set for all relevant minima and selected first- and second-order critical points on the tinprotonated and protonated potential energy surfaces (PES’s) of vinyl alcohol, methyl vinyl ether and 1,3-butadien-l-01 were determined. The proton affinities for each minimum isomer on the PES’s of these compounds were also determined. These three systems were chosen as initial compounds to model the highly potent mutagenic “fecapentaenes” which are found in the bowel mucosa of people who have a high risk of developing colon cancer. These model compounds were chosen for two reasons: (1) to determine if a simplified glycerol moiety (i.e. a methyl group in methyl vinyl ether) can be further simplified to a hydrogen atom as in vinyl alcohol, and (2) to compare and contrast the differences obtained in the PES when the double bond moiety in vinyl alcohol is extended to a conjugated carbon-carbon double bond system as in 1,3-butadien-l-01. The calculations reveal that the glycerol moiety of the enol ether type compounds may be simplified to a hydrogen atom using enol aldehyde compounds. In general, the PES’s of the model fecapentaene compounds behave as would be predicted by chemical intuition, i.e. secondary carbonium ions are found to be more stable than primary carbonium ions, and the anti or trans configurations for (CCCC) , (CCCO) and (HOCC) torsional angles are favored over the syn or cis configurations respectively (unless the cis/syn configurations are part of a ring system formed by H-bond or covalent type bonds). Configurations about carbon-carbon double bonds favor trans over cis, and fiily, when three-, five- and six-membered rings can form, the calculations reveal that in all likelihood they will do so. The most important features at each basis level were that the energy barriers for methyl, methoxyl and hydroxyl rotations were very low, corresponding to virtuahy free rotations, and that the energy differences between conformers of a given isomer were small. The geometries determined by the 3-21G basis set should be superior to those determined with the STO-3G basis set, and some unusual features were present with the STOdG basis set, especially when the protonation site was oxygen.

0166-1280/88/$03.50

0 1988 Elsevier Science Publishers B.V.

360

INTRODUCTION

The compounds responsible for colon cancer were identified in the material with which the intestine walls are in constant contact (i.e. feces) using a bacterial assay of mutagenicity [ 11. The search for such substances led to the discovery of four novel compounds named the fecapentaenes: fecapentaene-14 (I) and three stereoisomers of fecapentaene-12 (II) [ 2-41.

R = CH,-CH-CH,AH I-(l-glycero)

R’ =

-KH,),CH:,

AH temdeca

-1.3.5.7.9

- pentoene

R’

R\o-

at’)

R’ = -CH,-CH,

l-(l-giycero)dodeco-

1.3.5,7.9-pentoene

These provisional names were coined to indicate that the compounds are from the fecal stream and have a “pentaene” moiety [ 31. The important structural features of the fecapentaenes include the following: (1) they are enol ethers of polyunsaturated conjugated aldehydes and (2) they have a conjugated array of five double bonds as part of the enol ether system. These glyceryl ether lipids are very potent, directly-acting mutagens that do not require metabolic activation and are suspected to be the cause of colon cancer [ 51. In addition to the mutagenicity, they exhibit a number of effects on bacterial or mammalian somatic cells based on damage to DNA or impairment of the repair to DNA [ 61. Such properties are usually correlated with carcinogenicity. It has also been shown that the S-enantiomer of (IIIa) is produced by colon bacteria [ 71, and that there is a correlation between the excretion of this mutagen and the populations with a high risk of developing colon cancer [ 81. HO

H

361

It is believed that the carbocation generated by protonation of the fecapentaene is the source of the mutagenicity of these compounds. The biologically active pathway of the carbocation is, as yet, unknown. However, the charge delocalized, highly stabilized carbocation can be formed by hydrolysis of the enol ether system in aqueous acid. The generated carbocation (IV) will undergo a series of rapid rearrangements and transformations [ 91.

Most chemical carcinogens are electrophilic type reagents [ lo], and the carbocations of type (IV) and homologated polyenic type cations have been shown to be reactive as electrophiles in a variety of reactions [ 111. Provided that the carbocation functions as the ultimate mutagen, it is suggested (and proved) with good evidence, that the glyceryl moiety will play no significant role in the mechanism [ 91. However, it may modulate the mutagenic activity, e.g. by formation of an acetal (VI) via an intramolecular quenching of the cation (V) or by transportability of the fecapentaenes (I) and (II) across membranes [ 91.

I

CH20H

(PI

0

Pl--0

CHPH

R’

\\\A

b-i

(XII)

Krepinsky and co-workers [ 91 tested methyl enol ethers and aldehydes with a varying number of conjugated double bonds for mutagenicity. The results indicated the following: (1) the mutagenicity of methyl enol ethers (in Ames assay) increases with an increased number of double bonds, and (2) although the aldehydes are mutagenic, they are less active than the enol ethers. The fecapentaenes are known to be unstable when exposed to light, oxygen and protic media. Furthermore, the protonated products present experimental

362

problems because of rapid rearrangements of the initial protonated species. The longer the unsaturated chain, the more rapid the rearrangements. It is not known how the delocalization of the charge affects the stability and reactivity of the intermediates or how it affects the initial carbocation formation. A theoretical treatment of this type should contribute to our understanding. This study focuses primarily on the unconjugated system and it omits the glycerol moiety of the fecapentaene structure. In particular, the protonated and unprotonated conformers of the model compounds (methyl vinyl ether (VII), and the enols of the aldehydes with the general structures (VIII), having one (i.e. vinyl alcohol) and two (i.e. 1,3-butadien-l-01) carbon double bonds) are studied.

CH3

H\C--CH CH,-0’

-

’

XII

These model compounds were chosen for two reasons: (1) to determine if a simplified glyceryl moiety (i.e. a methyl group in methyl vinyl ether) can be further simplified to a hydrogen atom as in vinyl alcohol, and (2) to compare and contrast the differences obtained in the potential energy surface (PES) when the double bond moiety is extended to a conjugated carbon-carbon double bond system as in 1,3-butadien-l-01. Knowledge of equilibrium geometries and relative energies on the PES of model substances related to the fecapentaenes should be useful in determining the potential for tautomerism of the carbocation formed under mild protonation conditions. METHODOLOGY

Ab initio LCAO-MO-SCF calculations were performed utilizing the program MONSTERGAUSS [ 121 in conjunction with a GOULD 32/9705 minicomputer. The three basis sets used in this study consisted of the minimal STO-3G [ 131, split valence 3-21G [ 141 and the split valence with single polarization 6-31G* [ 151. The RHF method [ 161 was used for all closed shell systems. The geometries of the singlet ground state for all molecules considered were energy optimized by the optimally conditioned (OC) technique [ 171, excluding single point 6-

363

2-0-l vinyl

alcohol

3-o-j methyl-vinyl

4-0-l alcohol

1 3- butadien

- 1 - 01

Fig. 1. Naming convention for the isomers/conformers.

31G* energy determinations which were performed on the optimized 3-21G geometries. The critical points were determined by finite differences of gradients for every molecule computed at the STO-3G and 3-21G basis levels. The order checks were performed by evaluating the second derivatives (Hessian) matrix using small changes in the optimized dihedral angles, bond angles and bond lengths that would break any symmetry elements possessed by the molecule. In general most of the gradient optimizations were terminated when the gradient length (g)

Igl ={ [C(aEIdCh)21/N)1’2 (where qi are the internal coordinates and the sum is over the N optimized coordinates) was reduced below 0.0005 mdyne. This criterion usually yields structures to within 0.01 pm or 0.01’ of the theoretical optimum values [ 181. Initial geometries were taken from those that are predicted by the Valence Shell Electron Pair Repulsion Theory (VSEPR) [ 191 and bond lengths were taken from standard tables [ 201. The naming convention for the isomers/conformers of the three systems studied in this work is illustrated in Fig. 1. Each isomer is identified by a series of three digits separated by hyphens. The first digit, in the series of three, represents the number of carbon atoms in the molecule. The second digit indicates the protonation site of the molecule where the first protonation site begins at oxygen, with the subsequent protonation sites travelling down the carbon chain (see Fig. 1). A value of zero for the second digit indicates that the molecule is unprotonated. Finally, the third digit represents the conformer within a given series. This numbering scheme does not comply with IUPAC, but is used for simplicity. The present numbering scheme is applied to both the open chain and cyclic isomers. Within the illustrated PES schemes, some points worth mentioning include the following: (1) the location of the positive charges are shown so as to be in

364

accord with the selected valence structures presented; (2) because no account is taken of zero point vibrations in these energy calculations, the energy barrier between conformers is simply the difference in energy in conformers of different orders; (3) arrows are used to indicate the method or direction of rotations and inversions as prescribed by the order checks; (4) hydrogen atoms are not explicitly illustrated. Two general approaches were used in this work. The first approach was to compare the simplest of enol ethers (methyl vinyl ether ( MVE) ) with the enol of the corresponding aldehydes (vinyl alcohol) and the protonation of these systems. The second approach was to study the effects caused by increasing the olefinic double bond chain length from one to two unsaturated units (vinyl alcohol vs. 1,3-butadien-l-ol) . RESULTS AND DISCUSSION

Full structural details are available upon request for all optimized molecules on the critical points of the PES of the vinyl alcohol, methyl vinyl ether and 1,3-butadien-l-01 systems. The reader is also directed to ref. 21 for this information. Although there have been previous studies on the minima of the unprotonated vinyl alcohol [ 22,231 and methyl vinyl ether [ 241 systems, in this work we attempted to generate the potential energy surfaces of these species in order to obtain some understanding of the relative energies of the conformers of these protonated enol ethers with the general structure (IX).

for

n=

1.2

Unprotonated

(Ix)

andprotonated

vinyl alcohol

The PES’s of vinyl alcohol and its protonated isomers are illustrated in Figs. 2,3 and 4 at the STO-3G, 3-21G and 6-31G* basis levels, respectively. Figures 2,3 and 4 illustrate the computed total energies (hartree) and relative stabilities (kJ mol-’ ) for all computed conformers on the PES of protonated vinyl alcohol at each of the three basis levels used. Optimized parameters for all isomers at the STO-3G and 3-21G basis levels in the above three schemes can

365

Fig. 2. Computed total energies (hartree) and relative stabilities (kJ mol-‘) and protonated vinyl alcohol PES’s at the STO-3G basis level.

for the vinyl alcohol

Fig. 3. Computed total energies (hartree) and relative stabilities (kJ mol-’ ‘) for the vinyl and protonated vinyl alcohol PES’s at the 3-21G basis level. Fig. 4. Computed total energies (hartree) and relative stabilities (kJ mol-’ ) for the vinyl alcohol and protonated vinyl alcohol PES’s at the 6-31G* basis level.

366 TABLE 1 Calculated total energies (hartree) for all isomers/conformers on the PES of unprotonated and protonated vinyl alcohol Isomer

STO-3G

(2-0-l) (2-O-2)

Order

3-21G

Order

6-31G*

- 150.916677 - 150.913107

- 152.041764 - 152.036899

0 0

- 152.887547 - 152.884014

(2-l-l) (2-l-2) (2-l-3) (2-l-4)

-

151.289640 151.289212 151.287069 151.287165

- 152.353287

0

- 152.349566

1

(2-2-l) (2-2-2) (2-2-3) (2-2-4)

-

151.298461 151.232953 151.323170 151.219441

-

152.325613 152.295224 152.315223 152.281602

-

153.17366 153.151012 153.152511 153.138935

(2-3-l) (2-3-2) (2-3-3) (2-3-4)

-

151.323204 151.323170 151.321434 151.321461

-

152.367675 152.367700 152.366414 152.366590

-

153.224192 153.223478 153.221789 153.222717

be obtained from the authors upon request. Table 1 includes all computed total energies at the STO-3G and 3-21G basis levels and the single point energy determinations at the 6-31G* basis level. Table 2 summarizes the proton affinities (PA) of vinyl alcohol at the three basis levels. There is no known experimentally calculated proton affinity for vinyl alcohol. TABLE 2 Calculated proton affinities for the protonated vinyl alcohol isomers at the STO-3G, 3-21G and 6-31G* basis levels Isomer

Calculated proton affinities (kJ mol-‘) STO-3G

3-21G

6-31G*

(2-l-l) (2-l-2)

-978.2 -978.1

- 817.9

- 757.1

(2-2-l) (2-2-2)

- 1002.4 - 830.4

- 745.2 - 665.4

- 750.4 -691.7

(2-3-l) (2-3-2)

- 1067.3 - 1067.2

- 855.7 - 855.7

- 883.8 - 882.0

361

Vinyl alcohol CH, = CH-OH

For the unprotonated isomers at each level of theory, the syn (HOCC ) conformer was calculated to be more stable (i.e. conformer (2-O-l) was more stable than (2-O-2) ) . The energy differences between these two conformers were calculated to be 9.4 kJ mol-’ (STO-3G), 12.8 kJ mol-l (3-21G) and 9.3 kJ mol-’ (6-31G*). Both conformers maintained planar symmetry. However, the energetically more stable conformer (2-O-l) had a CC0 angle of approximately 126”, whereas the (2-O-2) conformer was closer to the expected 120” for molecules with sp2 hybridized carbon atoms. Protonated vinyl alcohol

Results for the protonated vinyl alcohol systems are in good agreement with the results of previous theoretical work [ 22,231 performed on the local minima of Figs. 2,3 and 4 only. These authors have calculated selected conformers on the PES for the protonated isomers. The three stable isomers of C,H,O+ have also been characterized in the gas pl%e [25]. Vinyloxonium cation (CH,= CH-ZHJ. At all three levels of theory the ( 2l-l ) quasi orthogonal conformer was determined to be more stable than the planar (2-l-4) conformer. The energy differences between the two conformers were found to be 6.5 kJ mol-’ (STO-3G) 9.8 kJ mol-’ (3-21G) and 8.7 kJ mol-’ (6-31G*). The preferred conformation of the vinyloxonium cation was rationalized in terms of a reduced tendency for electron donations into the a* system of C = C double bonds [ 261 from the oxonium moiety. This electron reorganization would lead to a valence structure with a formal double positive charge on oxygen.

CH2 = CH-:H,

-

:H, &HZ%,

The preferred orthogonal conformation (2-l-l) would be stabilized by hyperconjugative electron donation into O-H bonds. At the STO-3G level, two additional minima, (2-l-2) and (2-l-3)) were located on the PES. The critical points between the three minima (i.e. (2-1-l), (2-l-2), (2-l-3)) were not identified because the energy differences between these conformers are less than 6.7 kJ mol-’ on this surface. 2-Hydroxyethenium cation (OCH,-CHs-OH). Thepreferred2_hydroxyethenium cation was calculated to be the (2-2-2) conformer with the anti configuration about HOCC. The trans conformer (2-2-2) was determined to be 35.7 kJ mol-’ (STO-3G), 35.8 kJ mol-’ (3-21G) and 31:7 kJ mol-’ (6-31G*) more stable than the cis (2-2-4) conformer. Conformations in which the methylene plane is perpendicular to CC0 bonds collapse to form stable three-membered rings, without activation.

368

-

H.

“,, 0

/\

@

Hdc-c

$8

..H

OH

The three-membered rings were found to be very stable local minima in this subscheme (i.e. protonation at the first carbon site). The oxygen protonated oxirane (2-2-l) was found to be 172.0 kJ mol-l, 79.8 kJ mol-’ and 58.7 kJ mol-l more stable than the 2-hydroxyethenium cation (2-2-2) at the STO3G, 3-21G and 6-31G* basis levels, respectively. Although the three-membered ring formation is favored at the SCF level, it should be pointed out that this favored ring stability diminishes when the size of the basis set is increased. I-Hydroxyethenium cation (C&-&-OH). The (2-3-l) conformer in the 1-hydroxyethenium cation PES was found to be the most stable isomer of the protonated vinyl alcohols at all three basis levels. Some of the more interesting features of the 1-hydroxyethenium cation PES are that the methyl group favors the eclipsing of the C-O bond, and that the anti or tram configuration about the ( HOCC ) torsional angle is preferred over the cis configuration. Another interesting feature with an increase in the size of the basis sets is that a general decrease in the C-O bond length is observed, from 1.421 A (STO-3G) and 1.400 A (3-21G) to 1.282 A (STO-3G) and 1.265 A (3-21G), which may perhaps be attributed to the resonance structures CH,-;H-OH

-

CH,-CH=:H

The most important feature of the 1-hydroxyethenium cation PES is that it is very flat with respect to methyl and hydroxyl rotational energy barriers. For example, the total energy differences between the most and least stable conformers at the three basis levels are 4.6 kJ mol-l ( STO-3G), 3.4 kJ mol-’ (321G) and 6.3 kJ mol-l (6-31G*). The surfaces are so flat that- at the 3-21G level, for example, both the (2-2-2) and (2-3-l) conformers have the same computed energy. It can also be suggested that for energy barriers below 20.0 kJ mol-’ at room temperature, the methyl and hydroxyl rotations may be considered to be free rotations. The above PES’s have energy differences well below this level. General features of Figs. 2,3 and 4 In all three figures we note that the formation of rings (i.e. ( 2-2-3) and (22-1)) are local minima when protonation occurs at the first carbon site. How-

ever, the global minimum in all three schemes occurs when a secondary carbocation (1-hydroxyethenium cation) is formed by protonation at the terminal carbon site of vinyl alcohol. The other general feature that is observed in the PES of protonated vinyl alcohol is that the eclipsing of methyl groups with oxygen stabilizes the conformers. Finally, we observe that at the STO-3G and 3-21G basis levels, the PES’s are different. In particular, at the 3-21G level, the (2-l-2) and (2-l-3) conformers of the vinyloxonium ion both collapse to the (2-l-l) conformer. Methyl vinyl ether Figures 5-10 and their subschemes illustrate the Valence Shell Electron Pair Repulsion (VSEPR) structures for the conformers and isomers of the unprotonated and protonated methyl vinyl ether (MVE) calculated with the STO3G, 3-21G and 6-31G* basis sets. Within the above schemes the computed total energies (hartree) and relative stabilities (kJ mol-‘) are illustrated for all isomers and conformers thereof. Table 3 includes all computed total energies at the STO-3G and 3-21G basis levels and the single point energy determinations computed at the 6-31G* basis level. Table 4 summarizes the proton affinity for MVE at the various basis levels. The calculated minima on the 3-21G PES and the 6-31G* single point energy calculations are in close agreement with those found by Nobes and Radom

t241. Electron diffraction results for methyl vinyl ether reveal that a mixture of three conformers exists [ 271. These are the syn and anti forms with a planar skeleton of heavy atoms and a gauche form with a (COCC) torsional angle of approximately 150” or higher. This agrees with the findings of our work where three conformers were found to exist (as illustrated in Figs. 57 and 9) for the unprotonated MVE. Spectroscopic methods [ 28,291 and electron diffraction results [ 301 are in good agreement with our findings where the syn conformer ( 3-O-4 ) with the planar heavy atom skeleton and a (CCOC ) torsional angle of 0” was found to be the most stable MVE conformer. Experimental evidence [ 28,291 suggests that thegauche conformer of MVE lies approximately 4.8 kJ mol-’ above the stable syn conformer. In our calculations, the gauche conformer (3-O-5) was found to be approximately 3.9 kJ mol-l, 13.6 kJ mol-’ and 9.2 kJ mol-’ above the syn conformer (3-O-4) at the STO-3G, 3-21G and 6-31G* basis levels, respectively. Table 5 illustrates the geometrical parameters from the electron diffraction results [ 271 and the optimized parameters from our calculations at the STO3G and 3-21G optimized basis levels. From the electron diffraction and spectroscopic data, the gauche conformer

Fig. 5. Computed total energies (hartree) and relative stabilities (kJ mol-’ ) for the unprotonated and 0-protonated methyl vinyl ether PES’s at the STO-3G basis level. Fig. 6. Computed total energies (hartree) and relative stabilities (kJ mol-‘) methyl vinyl ether PES’s at the STO-3G basis level. r

for the C-protonatsd

Fig. 7. Computed total energies (hartree) and relative stabilities (kJ mol-‘) and 0-protonated methyl vinyl ether PES’s at the 3-21G basis level.

for the unprotonated

Fig. 8. Computed total energies (hartree) and relative stabilities (kJ mol-‘) methyl vinyl ether PES’s at the 3-21G basis level.

for the C-protonatad

Fig. 9. Computed total energies (hartree) and relative stabilities (kJ mol-‘) and 0-protonated methyl ether vinyl PES’s at the 6-31G* basis level. Fig. 10. Computed total energies (hartree) and relative stabilities ated methyl vinyl ether PES’s at the 6-31G* basis level.

for the unprotonated

(kJ mol-‘)

for the C-proton-

of MVE with a torsional angle of approximately 150” or higher is in good accord with our calculations at the various basis levels. The PES’s of unprotonated MVE are similar at all basis levels with the exception of the 3-21G basis level where the torsional angles of the unprotonated MVE are considerably changed and where the energy difference between isomers changes from approximately 4.0 kJ mol-’ to 14.0 kJ mol-l. At the 6-31G* basis level, the conformer (3-O-2) becomes slightly more stable than the (3-O-5) conformer (by approximately 0.1 kJ mol-‘) . However, this energy difference is negligible owing to the flatness of the PES. Protonated methyl vinyl ether It should be emphasized that care must be taken in the interpretation of the results for some of the order checks, which may seem to be ambiguous owing to the breakdown of the approximation formula for calculating the second derivative by finite differences. Use of double sided steps in calculating the Hessian matrix should have reduced the numerical errors. However, there may still be errors associated with the formulae when the PES is very flat.

372 TABLE 3 Calculated total energies (hartree) for ail isomers/conformers on the PES of protonated and unprotonated methyl vinyl ether Isomer

STO-3G

(3-0-l) (3-O-2) (3-O-3) (3-O-4) (3-O-5)

- 189.492586

- 190.848354

-

189.4905468 189.490891 189.496986 189.495489

-

190.849869 190.850265 190.855295 190.850095

-

191.908676 191.910695 191.908465 191.914137 191.910640

(3-l-l) (3-l-2) (3-l-3) (3-l-4) (3-l-5) (3-l-6) (3-l-7)

-

189.881710 189.881989 189.878674 189.880754 189.884686 189.882417 189.884507

-

191.178363 191.179066 191.175630 191.178255

-

192.215158 192.216962 192.213681 192.216410

(3-2-l) (3-2-2) (3-2-3) (3-2-4) (3-2-5) (3-2-6)

-

189.815085 189.819382 189.805047 189.797462 189.874034 189.896258

(3-3-l) (3-3-2) (3-3-3) (3-3-4) (3-3-5) (3-3-6) (3-3-7) (3-3-8)

-

189.919086 189.918086 189.920835 189.919856 189.917052 189.915520 189.915974 189.916888

Order

1 0 1 3” 1 0

3-21G

Order

6-31G*

- 191.182119

0

- 192.219953

-

191.110928 191.113987 191.101683 191.097108 191.146737 191.155896

1 0 1 2” 1 0

-

192.179642 192.182660 192.163815 192.165403 192.199393 192.215824

-

191.198347 191.196868 191.199522 191.198056 191.197148 191.196809 191.196612 191.197148

-

192.265710 192.264421 192.267213 192.265972 192.263389 192.262222 192.262230 192.262833

“Unsure of order due to the lack of numerical accuracy of the method used in calculating the second derivatives.

All minima on the PES’s of protonated MVE in Figs. 7-10 at the 3-21G and 6-31G* basis levels are in good agreement with results previously reported by Nobes and Radom [ 241. Table 3 summarizes the relative energies for all minima on the protonated MVE surface at the various basis levels and levels of theory. Table 3 includes both results from this study and that of Nobes and Radom [ 241. The Hartree-Fock (H-F) STO-3G results are from this work exclusively. The 3-21G and 6-31G* values found in this work agree exactly with the results of Nobes and Radom.

373 TABLE 4 Calculated proton affinities for the protonated methyl vinyl ether isomers at the STO-3G, 3-21G and 6-31G* basis levels Isomer

Calculated proton affinitied (kJ mol-‘) STO-3G

3-21G

6-31G*

(3-l-5) (3-l-6) (3-l-7)

-1017.9 -1011.9 - 1017.4

- 858.1

-862.9

(3-2-2) (3-2-6)

- 846.4 - 1048.3

-679.2 - 789.2

- 705.0 -792.1

(3-3-3) (3-3-5)

-1112.8 - 1102.9

-903.8 - 897.5

- 972.0 -917.0

An examination of the energy differences between the isomers within a basis level in Table 3 can be used to assess the basis sets. If an increase in relative energy is observed when the basis level is improved, then the larger basis set should be used in the calculations. Taking the 1-methoxyethenium cation as the overall minimum energy isomer, several notable features can be observed in Table 3. An important feature is that with the exception of three anomalous points (the oxygen protonated MVE at the STO-3G and 6-31G* levels and the 0-methyloxiranium cation at TABLE 5 Experimental and calculated geometrical parameters for methyl vinyl ether ( 3-O-4)a Parameter

Experiment

STO-3G

3-21G

[271 c=c Cz-0, G-0, C,-H

1.341 1.360 (3) 1.428 (3) 1.088 (14)

G-H, G-H, CrHw

1.088 (14) 1.105 (14)

< cot < cc0
118.3 (1) 127.7 (1.4) 114.8 (1.2)

1.3128 1.3920 1.4333 1.0777 1.0767 1.0892 1.0913 1.0939

1.3158 1.3699 1.4368 1.0704 1.0706 1.0704 1.0775 1.0832

113.7541 129.4815 106.6348

119.1499 128.0837 105.9403

*Estimated error given in parentheses [ 271.

374

the STO-3G level) the energy differences between isomers increase as the size of the basis set is increased. The oxygen protonated MVE was determined to be less stable than the 0-methyloxiranium cation at the STO-3G level, and surprisingly, it seems to be destabilized at the 6-31G* basis level. The stability of the 0-methyloxiranium cation is found to be overestimated at the STO-3G level, due to overlap stabilization [ 311 which is favored by sp basis sets. Results for HF/6-31G* single point energy calculations reveal a larger energy difference between isomers than that previously computed for MP3-6-31G*. On the basis of the results in Table 3 and the previous discussion, it appears that the best basis set to use for the generation of the protonated methyl vinyl ether PES is the 3-21G split valence basis set. The large energy differences between the isomers and the absence of anomalous results support this choice.

Ethenylmethyloxonium cation (CH, = CHEHCHJ The PES of the ethenylmethyloxonium cation appears to be consistent at all three basis levels used in this work, with the exception of a few discrepancies. The first of these is that the (3-l-l) conformer was determined to be a first-order critical point at the STO-3G level, when perhaps it should be a second-order critical point. The small value calculated for the second eigenvalue (e,,=O.O02671) for (3-l-l) may perhaps account for the fact that this conformer is a first-order critical point. The minima for the ethenylmethyloxonium cation were found to be asymmetric with a near orthogonal or pyramidal orientation of C (3) OH (4) with respect to the CC0 plane. The orthogonally oriented minima were calculated to be 7.08 kJ mol-’ (STO-3G), 8.17 kJ mol-’ (3-21G) and 8.07 kJ mol-’ (631G*) more stable than the corresponding planar first-order critical points. Another discrepancy between the optimized minima is observed between the STO-3G and 3-21G basis levels. At the STO-3G level, there are three local minima (3-l-5)) (3-l-6) and (3-l-7) all of which are skewed conformers whose relative energies lie within 5.9 kJ mol-’ of each other. At the 3-21G level, these three conformers all collapse to a single minimum geometry. The energy surfaces of the conformers of the ethenylmethyloxonium cation at all three levels of theory were found to be very flat with an energy range of 15.8 kJ mol-’ (STO-3G), 17.0 kJ mol-’ (3-21G) and 16.7 kJ mol-’ (6-31G*). Furthermore, there were problems encountered when attempting to interpret the energy differences between the minimum of the ethenylmethyloxonium cation and that of the most stable isomer in the overall PES (the (3-3-3) conformer of the 1-methoxyethenium cation). The energy differences are 94.9 kJ mol-l (STO-3G), 35.7 kJ mol-’ (3-21G) and 124.1 kJ mol-1 (6-31G*). It is difficult to assess whether the energy calculated at the 3-21G level is too low, or whether the one calculated at the 6-31G* level is too high, since no experimental data are available.

375

2-Methoxyethenium cation (CH,-0-CH,-CH,B) There appear to be two surfaces for the 2-methoxyethenium cation. The first surface has a minimum energy (3-2-2) conformer that is a primary carbocation with the positive charge /3 to the oxygen atom and with an anti configuration for the (COCC) torsional angle. The second surface has a minimum where the primary carbocation collapses to a ring, the 0-methyloxiranium ion (3-2-6). The relative stabilities of this conformer over the open chain (3-2-2) isomer were computed to be 201.8 kJ mol-‘, 110.0 kJ mol-1 and 87.1 kJ mol-’ at the STO-3G, 3-21G and 6-31G* levels, respectively. The stability of the directly generated 0-methyloxiranium cation (3-2-6) remains to be tested experimentally [ 241. A problem associated with sp basis sets (like the ones used in this work) is that the stabilities of the ring isomers are overestimated. One observes, however, that as the size of the basis set is increased, the energy difference between the ring (3-2-6) and open chain conformer (3-2-2) is significantly reduced. Therefore, the ring conformer (3-2-6) is not as stable as the results suggest since rings are favored by sp basis sets. In addition Radom and Nobes [ 241 suggest that in an ICR experiment the initially formed 2-methoxyethenium cation (3-2-2) undergoes a 1,2-hydrogen shift to form the 1-methoxyethenium cation (3-3-3)) rather than undergoing ring formation to yield the O-methyloxiranium cation (3-2-6).

I-Methoxyethenium cation (CH,-0-ZH-CH,I For the 1-methoxyethenium cation we can envisage that the PES is divided into two subsurfaces for the syn and anti conformers (or (COCC) torsional angles of 0 ’ and 180” ) . A number of difficulties are encountered at all three basis levels when the (COCC) torsional angle is 0.0”. Firstly, the surface between the (3-3-5)) (33-6)) (3-3-7) and (3-3-8) conformers is very flat. Secondly, this becomes even more of a problem as the basis set is improved. These flat surfaces result in numerical errors in the calculation of the second derivatives, which may lead to problems in the interpretation of the order of the critical points. The outcome of these errors implies the following problem with the topology. There appear to be two second-order critical points missing from the determined surface. However, because the barriers for the methyl rotations are essentially zero, and since the anti PES for this conformer was found to be more stable, the missing second-order critical points were not sought. Since the subsurface of the 1-methoxyethenium cation with a (COCC) torsional angle of 180o is more stable than that with a (COCC) torsional angle of 0” and because the PES of the latter is so flat, this will not be considered further. The most stable conformer of the 1-methoxyethenium cation, and of the

376

overall PES of protonated MVE was determined to be (3-3-3) with an anti configuration about (COCC). This conformer was calculated to be 10.4 kJ mol-’ (STO-3G), 6.2 kJ mol-l (3-21G) and 10.0 kJ mol-’ (6-31G*) more stable than the lowest syn COCC (3-3-5) conformer. The barriers for both methyl and methoxy rotations for the l-methoxyethenium cation PES were found to be less than 7.0 kJ mol-l at all the basis levels, corresponding to essentially free rotation. Furthermore, the hydrogen atoms eclipse with the heavy atom skeleton for both methyl and methoxy groups. Comparison of vinyl alcohol and methyl vinyl ether Since the methoxyl group in methyl vinyl ether did not have a significant impact on the results of the PES in comparison with those of vinyl alcohol, the authors feel that they were justified in neglecting the alkyl or glyceryl moieties of the larger systems investigated in this study. These moieties may also be neglected in future studies. In general, when protonation occurs at oxygen, both the MVE and vinyl alcohol systems tend to an orthogonal or pyramidal configuration at the oxygen centre. Furthermore, as the basis set is increased from STO-3G to 3-21G, a single minimum is found at the higher basis level as opposed to multiple minima at the lower basis level. Both systems behave as expected from chemical experience. For example, an anti configuration is preferred over a syn configuration and secondary carbocations are found to be more stable than primary carbocations. Furthermore, the isomer with the electron deficient cationic carbon next to the oxygen is more stable than isomers in which the carbocation is further away from the oxygen. Finally, in both systems, methyl and hydroxyl hydrogens eclipse with the heavy atom system. Unprotonated and protonated 1,3-butadien-l-01 Figures 11-28 and their subschemes illustrate the computed total energies (hartree) and relative stabilities (kJ mol-’ ) for all computed conformers and isomers on the PES of protonated 1,3-butadien-l-01 at the STO-3G, 3-21G and 6-31G* basis levels. The single points energy determinations at the 6-31G* basis level as well as computed total energies at the STO-3G and 3-21G basis levels are tabulated in Table 6. Table 7 summarizes the proton affinity of 1,3-butadien-l-01 at the three basis levels. There are no known experimental or theoretical results available for the protonated and unprotonated isomers of 1,3-butadien-l-01.

Fig. 11. Computed total energies (hartree) and relative stabilities (kJ mol-‘) dien-l-01 and 1,3-butadienyloxonium cation PES’s at the STO-3G basis level. Fig. 12. Computed total energies (hartree) and relative stabilities (kJ mol-‘) lH-1,3-butadienium cation PES at the STO-3G basis level.

for the 1,3-buta-

for the l-hydroxy-

+-4-t

T

2.2

*_ ___L I -227.2661

IJrcP

I

__+-__

I

Fig. 13. Computed total energies (hartree) and relative stabilities (kJ mol-‘) 2H-1,3-butadienium cation PES at the STO-3G basis level.

for the l-hydroxy-

Fig. 14. Computed total energies (hartree) and relative stabilities (kJ mol-‘) 2H-1,3-butadienium cation PES at the STO-3G basis level.

for the 4-hydroxy-

3..* _ I

7.ZKJrml-’

T *I “r “Ij; ‘3G:4-5_6

z,KJ”c-

4-5-5____

I

I

L

Fig. 15. Computed total energies (hartree) and relative stabilities (kJ mol-‘) SH-1,3-butadienium cation PES at the STG-3G basis level.

I

for the 4-hydroxy

Fig. 16. Computed total energies (hartree) and relative stabilities (kJ mol-’ ) for the I-hydroxy lH-1,3-butadienium cation PES at the STG-3G basis level.

Fig. 17. Computed total energies (hartree) and relative stabilities (kJ mol-’ ) for the 1,3-butadien-l-01 and 1,3-butadienyloxonium cation PES’s at the 3-21G basis level. Fig. 18. Computed total energies (hartree) and relative stabilities (kJ mol-‘) lH-1,3-butadienium cation PES at the 3-21G basis level.

for the 1-hydroxy.

.22,.8,~

_I-ZP=+

4

Fig. 19. Computed total energies (hartree) and relative stabilities (kJ mol-‘) 2H-1,3-butadienium cation PES at the 3-21G basis level.

for the l-bydroxy-

Fig. 20. Computed total energies (hartree) and relative stabilities (kJ mol-‘) 2H-1,3-butadienium cation PES at the 3-21G basis level.

for the 4-hydroxy-

_228.847~

,$iL SLI$_228,8i ”

____-----

b

2 e.

4-5-l

~

Fig. 21. Computed total energies (hartree) and relative stabilities (kJ mol ‘) for the 4-hydroxy2H-1,3-butadienium cation PES at the 3-21G basis level. Fig. 22. Computed total energies (hartree) and relative stabilities (kJ mol-‘) lH-1,3-butadienium cation PES at the 3-21G basis level.

for the 4-hydroxy-

I ?viI 3

4-1-6

-

-

-

-

-

-_x7,-

4-1-1 - ____

_

T I I’______ ’ ,

j

T

9.6umar

4-2-I

Fig. 23. Computed total energies (hartree) and relative stabilities (kJ mol-‘) dien-l-01 and 1,3-butadienyloxonium cation PES’s at the 6-31G* basis level. Fig. 24. Computed total energies (hartree) and relative stabilities (kJ mol-‘) lH-1.3-butadienium cation PES at the 6-31G* basis level.

for the 1,3-buta-

for the l-hydroxy-

Fig. 25. Computed total energies (hartree) and relative stabilities (kJ mol-*) for the l-hydroxylH-1,3-butadienium cation PES at the 6-31G* basis level. Fig. 26. Computed total energies (hartree) and relative stabilities (kJ mol-‘) BH-1,3-butadienium cation PES at the 6-31G* basis level.

for the I-hydroxy-

381

--y-

1 -2M.,,,c

-I

Fig. 27. Computed total energies (hartree) and relative stabilities (kJ mol-‘) SH-1,3-butadienium cation PES at the 6-31G* basis level.

for the 4-hydroxy-

Fig. 28. Computed total energies (hartree) and relative stabilities (kJ mol-‘) lH-1,3-butadienium cation PES at the 6-31G* basis level.

for the I-hydroxy-

1,3-Butadien-l-01 (CH, = CH-CH = CHOH) The optimized structures and relative energies of the 1,3-butadien-l-01 conformers were found to be consistent throughout the various basis sets used in this work. The most stable conformer (4-O-2) is planar with C, symmetry, possessing syn (HOCC) and trans (OCCC) torsional angles. The greater stability of the syn (HOCC ) dihedral angle compared with the anti ( HOCC ) dihedral angle was consistent throughout the basis levels for the 1,3-butadien-l-01 conformers. Another interesting feature of the 1,3-butadienl-01 surface was that the pseudo five-membered ring (formed by a hydrogen) in conformer (4-O-4) had no stabilizing effect on this 1,3-butadien-l-01 isomer. The present calculations show that the (4-O-4) conformer is 9.4 kJ mol-’ (STO-3G), 11.5 kJ mol-’ (3-21G) and 7.1 kJ mol-’ (6-31G*) less stable than the (4-O-2) conformer.

1,3-Butadienybxonium cation (CH,= CH-CH = CHEHj The 1,3-butadienyloxonium cation PES can be divided into two subsurfaces, the first having a cis configuration about the (OCCC) torsional angle (i.e. OCCC =O” ) and the second having a bans configuration about the ( OCCC) dihedral angle (i.e. (OCCC ) = 180’ ) .

382 TABLE 6 Calculated energies (hartree) for all isomers/conformers on the PES of 1,3-butadien-l-01 with STO-3G, 3-21G and 6-31G* basis sets Isomer

STO-3G energy

Order

3-21G energy

Order

6-31G* energy

(4-0-l) (4-O-2) (4-O-3) (4-O-4)

- 226.860950

0

- 228.498044

0

-226.863226 -226.859927 - 226.859653

0

- 228.499105

0

0

- 228.494705 - 228.497322

0

-229.772117 - 229.773798 - 229.770780 - 229.771088

(4-l-l) (4-l-2) (4-l-3) (4-l-4) (4-l-5) (4-l-6) (4-l-7) (4-l-8)

- 227.243997 -227.239469 -227.241087 - 227.242210 - 227.238426 -227.240737 - 227.241077 -227.241134

0

- 228.817314 - 228.810897

0

1

- 230.069941 - 230.063698

- 228.810637 - 228.818410

1 0

- 230.063408 - 230.069867

(4-2-l) (4-2-2) (4-2-3) (4-2-4) (4-2-5) (4-2-6) (4-2-7) (4-2-8)

- 227.243427 - 227.240736 - 227.226964 - 227.221359 - 227.243890 -227.213631 - 227.222349 - 227.234945

0 0 1 1 0 IS 1 0

- 228.815614 - 228.809374 - 228.795099 - 228.794153 -228.815534 - 228.781757 -228.787447 -228.801774

0 0 1 1 0 1” 1 0

-230.096148 -230.092488 - 230.080254 - 230.079286 - 230.093270 - 230.066761 -230.072142 - 230.084499

(4-3-l) (4-3-2) (4-3-3) (4-3-4) (4-3-5) (4-3-6) (4-3-7) (4-3-8) (4-3-9) (4-3-10) (4-3-11)

- 227.266499 - 227.261354 - 227.258198 - 227.258576 - 227.251077 - 227.256965 -227.260157 - 227.255723 - 221.255965 - 227.255659 - 227.252487

0 0 1 1 2 2 1 2” 2” 1” la

- 228.828630 -228.820912 -228.816896 -228.817915 - 228.815314 - 228.815601 - 228.819926 - 228.814679 - 228.814457 - 228.814506 - 228.811684

0 0 1 1 2 2 1 1” 1” 1” 1”

-230.110998 -230.104192 - 230.099542 -230.100355 -230.097816 - 230.098648 -230.102645 - 230.098410 - 230.097651 - 230.097562 - 230.095149

(4-4-l) (4-4-2) (4-4-3) (4-4-4) (4-4-5) (4-4-6) (4-4-7) (4-4-8) (4-4-9) (4-4-10) (4-4-11) (4-4-12) (4-4-13)

-227.284801 - 227.285638 - 227.188430 -227.187878 -227.189084 - 227.189259 -227.32844 -227.279973 -227.326100 -227.193990 -227.185184 -227.194514 -227.184394

0 0 1 1 2 2 0 0 1 1 1 2” 2”

-228.828659 -228.825523 -228.759525 -228.759677 -228.761937 -228.762918 -228.846601 - 228.820402 - 228.846490 - 228.771525 - 228.759311 - 228.774422 - 228.759354

0 0 1 1 2 0 0 1 1 1 1 2 2

- 230.114233 - 230.114557 - 230.041612 -230.0401271 - 230.045152 - 230.045362 - 230.099936 - 230.108381 - 230.098639 -230.049251 - 230.039501 - 230.053002 -230.041385

0

1” 1” 0 la 0 0 1

0

_

383 TABLE 6 (cont.)

Isomer

STOdG energy

(4-5-l) (4-5-2) (4-5-3) (4-5-4) (4-5-5) (4-5-6) (4-5-7) (4-5-8)

-227.297757 -227.290856 - 227.295839 - 227.288858 -227.298398 -227.297534 -227.296431 -227.295638

Order

Order

3-21G energy -

228.855827 228.847296 228.853840 228.845298 228.854926 228.854039 228.852930 228.852160

6-31G* energy - 230.136474 - 230.129333 - 230.134076 - 230.126881 - 230.138726 -230.138940 -230.136341 - 230.136667

“Unsure of order due to the lack of numerical accuracy of the method used in calculating the second derivatives.

The most stable conformer with the truns (OCCC) configuration was the (4-l-l ) conformer, with an orthogonal orientation of the oxonium moiety with respect to the planar heavy atom skeleton. Similarly, for the cis (OCCC) configuration an orthogonal orientation of the oxonium moiety stabilized the isomer as illustrated by the (4-l-6) and (4-l-7) conformers. Although the (4-16) conformer was 1.0 kJ mol-’ less stable than the (4-1-7) conformer at the TABLE 7 Calculated proton affinities for the protonated 1,3-butadien-l-01 minima isomers Isomer

Calculated proton affinities ( kJ mol-’ ) STO-3G

3-21G

6-31G*

(4-l-l ) (4-l-6 )

-999.7 -991.2

- 835.5 - 838.3

- 777.5 - 777.3

(4-2-l ) (4-2-5 )

- 998.2 - 999.4

-831.0 - 830.8

- 846.3 - 838.8

(4-3-l) (4-4-l ) (4-4-2 )

- 1058.8 - 1106.8 - 1109.0

- 865.19 - 865.2 - 857.0

- 885.3 -893.9 -894.7

(4-4-7 ) ( 4-4-8 )

- 1225.1 - 1094.2

-912.4 - 843.6

- 856.23 - 878.4

(4-5-5 ) (4-5-l)

- 1142.5 - 1140.9

- 934.2 - 936.6

-958.1 -952.2

384

STO-3G level, at the 3-21G level, the (4-l-7) and (4-l-8) conformers of the 1,3-butadienyloxonium cation both collapsed to the (4-l-6) conformation. Overall, the (4-l-l) conformer with a truns (OCCC) configuration about the heavy atom skeleton was found to be the most stable isomer of the 1,3butadienyloxonium cation PES at the STO-3G and 6-31G* basis levels. The (4-l-6) conformer was 2.9 kJ mol-’ more stable than the (4-l-l) conformer at the 3-21G level; however, this energy difference may be regarded as negligible and insignificant. For the truns ( OCCC) configuration at the 3-21G basis level both the (4-l-3) and (4-l-4) conformers collapsed to the (4-l-l) conformer. At the 3-21G level, the problem with the orthogonal conformers with syn (HOCC) configurations observed at the STO-3G level is alleviated because the (4-l-3) and (4-l-7) conformers collapse to the (4-l-l) and (4-l-6) conformers, respectively, with an anti (HOCC) configuration. The 3-21G surface was found to be more simple and straightforward than the STO-3G PES. Of the three basis levels used, it was the least shallow with respect to energy differences amongst the conformers and was the simplest to interpret. 1-Hydroxy-lH-1,3-butadienium

cation (H&=

CH-EH-CH,-OH)

The PES of the 1-hydroxy-lH-1,3-butadienium cation can be divided into two subsurfaces with respect to syn and anti (CCCC) torsional angles. There are no unusual features in the PES of the secondary carbocations of the 1-hydroxy-lH-1,3-butadienium cation. The energy difference between conformers, with respect to hydroxyl rotations, were determined to be significantly larger than the energy differences between isomers with syn and anti (OCCC) torsional angles. For the 1-hydroxy-lH-1,3-butadienium cation PES with an anti (CCCC) configuration, the (4-2-l) isomer with a syn (OCCC ) dihedral angle was computed to be more stable (by 7.1 kJ mol-l (STO-3G), 16.4 kJ mol-l (3-21G) and 9.6 kJ mol-’ (6-31G*)) than the (4-2-2) isomer with a (OCCC) torsional angle of 180’. The added stability of the syn (OCCC ) configuration may be due to the stability of the pseudo five-membered ring in the (4-2-l ) isomer (formed by the hydrogen bond) as compared with the unfavorable H-H interaction in the pseudo six-membered ring of the (4-2-3) conformer. &

(4-2-l)

/$

(4-2-3)

385 TABLE 8 Optimized bond angles for pseudo five-membered ring (4-2-l) and pseudo six-membered ring (42-3) Angle (deg )

HI-O& O&-C, C&-C, C&-C,

(4-2-l)

(4-2-3)

STO-3G

3-21G

STO-3G

3-21G

108.19 123.30 118.77

107.70 122.26 118.30

107.08 120.40 128.24 121.06

117.53 120.10 126.76 121.80

The angles in the pseudo five-membered ring (4-2-l) are compressed relative to the (4-2-3) conformer which has an unfavorable H-H interaction. Table 8 summarizes the optimized bond angles for the (4-2-l) and (4-2-3) conformers at the STO-3G and 3-21G baais levels. With these results, it seems that this pseudo ring formation (formed by the hydrogen bond) may perhaps be favored for the 1-hydroxy-lH-1,3-butadienium cation. For the 1-hydroxy-lH-1,3-butadienium cation PES with a syn (CCCC) torsional angle, the syn ( OCCC ) configuration was found to be more stable than configurations with anti (OCCC) dihedral angles. The most important features of the 1-hydroxy-lH-1,3-butadienium cation PES with the syn (CCCC) configuration are as follows. (1) The pseudo six-membered ring formed by a hydrogen type bond in the isomer (4-2-5) decreases in stability with respect to the pseudo five-membered ring conformer (4-2-l) as the size of the basis set is increased. At the STO-3G basis level, the pseudo six-membered ring conformer (4-2-5) was computed to be 1.2 kJ mol-’ more stable than the pseudo five-membered ring conformer (4-2-l ) . At the 3-21G and 6-31G* basis levels, the (4-2-5) conformer was computed to be less stable by 0.2 kJ mol-l and 7.6 kJ mol-l, respectively. (2 ) With the exception of the (4-2-5) conformer (which was more stable than the (4-2-l) conformer at the STO-3G basis level) the conformers of the syn (CCCC) PES of the 1-hydroxy-lH-1,3-butadienium cation were determined to be less stable than those with anti dihedral (CCCC) angles. I-Hydroxy-2H-1,3-butadienium cation (CH&H-CI&-?kX-IJ The PES of the 1-hydroxy-2H-1,3-butadienium cation can be divided into two subsurfaces, i.e. those with syn and anti (CCCC) torsional angles. There were some interesting features and results found for the l-hydroxy2H-1,3-butadienium cation surface with the anti (C&C) dihedral angle configuration. Firstly, this secondary carbocation, with the positive charge cen-

386

tered cy to the hydroxyl oxygen, was found to be more stable than the 1,3butadienyloxonium cation and the secondary 1-hydroxy-lH-1,3-butadienium cation. The other interesting feature of this surface was that although the firstand second-order critical points were planar with C, symmetry point groups, the local minima (conformers (4-3-l) and (4-3-2)) were found to possess skewed carbon atom backbones. This means that the carbon skeleton tends to form a helical type structure. In general, there is good agreement between the basis sets for the l-hydroxy2H-1,3-butadienium cation PES. The surface itself is consistent with respect to the determined order for the conformers in so far as the required parametric changes prescribed by the order checks lead to the minima on the PES. The (4-3-l) configuration with a syn (OCCC) torsional angle was calculatedto be 16.6 kJ mol-’ (STO-3G), 22.9 kJ mol-l (3-21G) and 21.9 kJ mol-’ (6-31G*) more stable than the (4-3-7) conformer with an anti (OCCC) dihedral angle. The optimized parameters are in good agreement with the valence structures represented in Fig. 17. An important parametrical feature is that both minima ( (4-3-l) and (4-3-2) ) maintain their double bond length at the C = C bond /3 to the positive carbon atom. This feature is interesting because the double bond length is preserved in the helical section of the oletinic chain. The most notable features of the PES of the 1-hydroxy-2H-1,3-butadienium cation with syn (CCCC) dihedral angles include the following. Firstly, the conformers with the anti (OCCC) torsional (i.e. (4-3-8) and (4-3-9)) are slightly more stable than those with the syn (OCCC) torsional (4-3-10) and (4-3-11) ) . Secondly, they are less stable than those with the anti (CCCC) torsional angle configurations. Finally, at both the STO-3G and 3-21G basis levels there are difficulties encountered with the determined orders, most likely as a result of the flatness of the PES’s. One way to resolve this problem may be to optimize these structures at the 6-31G* basis level and see what difference this may make. 4-Hydroxy-2H-1,3-butadienium cation (HO-CH=CH-CH,-CH,O) The PES of the 4-hydroxy-2H-1,3-butadienium cation can be divided into two subsurfaces, one corresponding to conformers with a trans (OCCC) torsional angle of 180”, and the other corresponding to conformers with a cis (OCCC) dihedral angle of 0.0”. The most important feature of the trans (OCCC) conformers of the 4-hydroxy-2H-1,3-butadienium cation is that they collapse to the symmetric (C,) , three-membered ring conformers (4-4-l) and (4-4-2). The (4-4-2) conformer was found to be 2.2 kJ mol-’ and 0.8 kJ mol-l more stable than the (4-4-l) conformer at the STO-3G and 6-31G* basis levels, respectively. At the 3-21G level, the (4-4-l ) conformer was calculated to be 8.2 kJ mol-’ more stable

387

than the (4-4-2) conformer. One would expect the (4-4-2) conformer to be more stable on the basis of steric hindrance arguments alone. The parameters associated with the three-membered ring conformers (4-41 ) and (4-4-2)) appear to be intuitively reasonable where the C = C double bond is elongated to accommodate the C-C bond formation to close the ring. The 4-hydroxy-2H-1,3-butadienium cations with the cis (OCCC) configuration have an intrinsic tendency to collapse to three-membered (4-4-8) and five-membered (4-4-7) ring isomers. The five-membered ring isomer (4-4-7) was calculated to be the most stable isomer overall on the protonated 1,3-butadien-l-01 PES at the STO-3G and 3-21G basis levels. At the 6-31G* level, the three-membered ring isomer (4-4-B)) was calculated to be 22.2 kJ mol-’ more stable than the (4-4-7) isomer. The stability of the (4-4-8) isomer over the (4-4-7) isomer at the 6-31G* level seems unreasonable on the basis of steric arguments alone. The stability of the five-membered ring isomer (4-4-7) cannot be rationalized in terms of the basis set favoring ring formation. Instead, the optimized geometric parameters and stereochemistry of the (4-4-7) isomer supports its credibility as being the most stable species on the PES. Furthermore, the planar heavy atom five-membered ring has an oxygen atom with the proper sp3 type hybridization and an unsaturated olefinic double bond at the a-j? position to oxygen. It appears that it is unlikely that we can disregard these five-membered rings as readily as the three-membered ring species. Hence, for any future work, the possibility of the formation of higher order ring systems should be investigated. For the cis (OCCC) heavy atom skeleton, the preferred (HOCC) configuration is anti, and vice versa for the anti heavy atom (OCCC) torsional angle. The energy difference between the syn and anti (HOCC

388 TABLE 9

AE for critical points on the 4-hydroxy-2H-1,3_butadienium cation PES Order one

(4-4-U) (4-4-10) (4-4-4) (4-4-3)

-

AE (kJ mol-‘)

Order two

(4-4-13) (4-4-12) (4-4-6) (4-4-5)

STO-3G

3-21G

6-31G*

-2.1 1.4 3.6 1.7

0.1 7.6 8.4 5.9

4.9 9.8 13.2 9.8

4-Hydroxy-lH-1,3-butadienium cation (CH,-EH-CH= CH-OH) The PES’s of the 4-hydroxy-lH-1,3-butadienium cation are remarkably similar at each of the three basis levels. The energy differences between conformers at each of the basis levels are almost equal in magnitude. The structural parameters of the optimized STO-3G and 3-21G geometries are also in close agreement. These secondary carbocations are interesting because the double bond at the a,/? position to the positive charge delocalizes into the positive carbon, with a resonance type stabilization, to form an allylic type cation

‘3, - ‘3, - ‘St, (4-5-5)

(4-5-5)

( 4-5-5)

where the C=C double bond length at the P,r position to the positive charge increases to approximately 1.42 A (STO-3G) and 1.36 A (3-21G). The C-C single bond at the a-/3 position to the positive charge shortens to approximately 1.36 A (STO-3G) and 1.35 A (3-21G) for all conformers of the 4hydroxy-lH-1,3-butadienium cation. For the 4-hydroxy-lH-1,3-butadienium cation, two subsurfaces can be defined by a cis and trans (OCCC) heavy atom skeleton as well as by the syn and anti (HOCC) dihedral angles. Trans (OCCC) conformers were found to be more stable than those with the ci.s configuration except at the 3-21G level, where the local minimum (i.e. (4-5-l)) was found to be 4.7 kJ mol-’ more stable than the (4-5-5) conformer with a trans (OCCC) configuration. This may be rationalized in terms of a pseudo five-membered ring which forms from H-bonding in (4-5-l).

389

TABLE 10 Comparison of internal angles in the (4-5-l)

(4-5-2)

(4-5-l)

Angle (deg) H,-0,-C, 0,-C& c,-c&c, H.&,-C,

H-BOND

and (4-5-2) conformers

STO-3G

3-21G

STO-3G

3-21G

120.98 120.71 118.75

121.43 120.72 118.47

112.34 128.90 124.13 120.89

122.03 129.30 124.06 120.64

I

(4-5-l)

This ring forming feature and hydrogen bonding is favored by sp-type basis sets. However, as the basis level is increased to 3-21G and 6-31G*, the stability of the (4-5-l) conformer is not destabilized with respect to the (4-5-5) conformer. Therefore it seems as if the cis ( OCCC ) configuration may be a favored conformer with its pseudo five-membered ring formed by a hydrogen bond. Furthermore, the internal angles are compressed (Table 10) in the (4-5-l) conformer in comparison with the (4-5-2) conformer which has an unfavored H-H interaction in a quasi six-membered ring as illustrated below.

-H

(4-5-Z)

(4-5-l)

In general, the anti ( HOCC ) torsional is favored over the syn configuration, with the exception of the (4-5-5) conformer (with a syn (HOCC) dihedral) that is 2.3 kJ mol-’ more stable than (4-5-6) at both the STO-3G and 3-21G levels. Since this energy difference is negligible, the anti (HOCC ) configuration was calculated to be approximately 15 kJ mol-’ and 2.0 kJ mol-l more stable than the syn (HOCC) configuration, for the truns and cis (OCCC) torsional angles, respectively. In summary, the secondary allylic type carbocations of the 4-hydroxy-lH1,3-butadienium cation PES are the most stable cations on the PES of proton-

ated 1,3-butadien-l-01, with the exception of the five-membered ring isomer (4-4-7). The 4-hydroxy-lH-1,3-butadienium cations were determined to be more stable than the secondary 1-hydroxy-2H-butadienium carbocations. The added stability is probably due to the resonance type stabilization of the positive charge as it involves a four atom conjugation with an allylic cation attached to an oxygen atom. With the exception of the low energy barriers of the hydroxyl and methyl rotations, the general features and characteristics of the PES of the 4-hydroxylH-1,3-butadienium cation and the geometrical parameters of the conformers are in good agreement with what would be predicted by chemical intuition. For example, the anti and truns torsional angles are favored for both the (HOCC ) and ( OCCC ) angles, respectively. Double bonds at the cy,/.?position to the positive charge are delocalized in a resonance fashion to stabilize the isomer. Finally, the methyl hydrogens tend to fall in the plane of the heavy atom skeleton to maintain C, symmetry in the conformations. Comparison of vinyl alcohol with 1,3-butadien-l-01 In summarizing the effects of increasing the double bond length by one unit (in going from vinyl alcohol to 1,3-butadien-l-01) the following generalities were observed. Firstly, for both unprotonated vinyl alcohol and 1,3-butadienl-01, the preferred (HOCC ) dihedral angle was determined to be the syn angle. Furthermore, all the unprotonatedconformers for both systems favored a planar configuration. When protonation occurs at oxygen, the topology of the PES is complex, especially at the STO-3G basis level for both vinyl alcohol and 1,3-butadienl-01. The surface simplifies as the basis set is increased to the 3-21G level. In both the protonated vinyl alcohol and 1,3-butadien-l-01 PES’s, the isomers with the positive charge on the oxygen atom tend to be the most stable. In the case of vinyl alcohol, the effect seems to be due to the conjugative effect of the oxygen lone pair, whereas for 1,3-butadien-l-01, the stability is a result of the resonance type delocalization of the positive charge into the (Y,/3 unsaturated olefinic chain as found with allylic type cations. Another common feature is that the protonated vinyl alcohol collapses to three-membered rings, and the protonated 1,3-butadien-l-01 cation collapses to both three- and five-membered rings when possible. It is unlikely that the three-membered rings can be regarded as stable intermediates on the true PES. However, one cannot exclude the larger five-membered rings formed from the larger olefinic chain as readily. Another interesting feature on the protonated 1,3-butadien-l-01 surface is that the carbon chain is found to skew at the y carbon when the protonation

391

site is j3 to the oxygen atom. In addition to this skewing feature, the olefinic double bond length is conserved in these species at both the STO-3G and 321G basis levels. Finally, it was observed that hydroxyl and methyl torsions were essentially free rotations, due to very low (less than 20 kJ mol-‘) energy barriers. Furthermore, it was determined that as the olefinic chain length was increased, the energy difference between hydroxyl and methyl rotamers decreased. CONCLUSION

One of the aims of this study was to compare the results at the various levels of theory, and to attempt to assess the levels required to describe adequately the PES of the model fecapentaene type compounds. The most important feature common to each of the three basis levels was that, within the accuracy of the calculations, the energy barriers for methyl, methoxyl and hydroxyl rotations were flat, and therefore they had virtually free rotation. Since the error in the SCF calculations, with respect to experimental heats of reaction, is determined to be 20 kJ mol-’ [ 311, the computed energy differences between conformers were generally found to be less than the accuracy of the SCF calculations, and hence cannot be considered precise in the absolute sense. However, the predicted trends can be meaningful in assessing the topology of a PES. The energy differences between conformers were found to be very small, and they were generally lowered as the length of the carbon chain was increased from vinyl alcohol to 1,3-butadien-l-01. Comparison of vinyl alcohol and methyl vinyl ether

Overall, the differences between the vinyl alcohol and methyl vinyl ether surfaces are very slight. At the unprotonated level, the PES of methyl vinyl ether has minima with gauche and planar heavy atom skeleton configurations. Although this is consistent with experimental findings [ 28-301 and previous calculations [ 241, it seems that the simpler unprotonated vinyl alcohol prefers a planar configuration. It should be pointed out that upon protonation of MVE, all isomers maintain a planar heavy atom skeleton. Apart from these differences the PES’s for protonated vinyl alcohol and MVE were found to behave similarly. For example, secondary type carbocations were found to be more stable than primary carbocations when the positive charge was ar to the oxygen atom. Furthermore, when protonation occurred at the oxygen atom, both vinyl alcohol and MVE surfaces behaved similarly at all basis levels. In particular, both systems had minimum energy conformers with an orthogonal orientation about the oxygen atom. Finally, it was observed that for both protonated vinyl

392

alcohol and MVE, the carbocation collapsed to form a stable three-membered ring isomer when the positive charge was p to the oxygen atom. On the basis of the results of this study on the protonated and unprotonated surfaces of vinyl alcohol and MVE, it appears that at a theoretical level the enol aldehydes can be used to model the fecapentaene type enol ethers. Comparison of vinyl alcohol with 1,3-butadien-l-01 Some interesting features are observed when the carbon chain length is increased by one olefinic unit from vinyl alcohol to 1,3-butadien-l-01. The first obvious feature is that the methyl and hydroxyl rotations decrease to essentially energy free rotations when the carbon chain is extended. Perhaps the most unusual feature is noted when protonation occurs /I to the oxygen atom (i.e. 1-hydroxy-2H-1,3-butadienium cation), where the carbon chain is found to skew towards the terminal end of the chain, whilst simultaneously maintaining an intact carbon-carbon double bond length. On the other hand, vinyl alcohol remains planar when protonation occurs /I to the oxygen atom. However, the secondary carbocation with a terminal methyl group is the most stable cation on the protonated vinyl alcohol surface, as is the case for the protonated 1,3-butadien-l-01 when protonation occurs at the last carbon atom of the olefinic chain. Both the vinyl alcohol and 1,3-butadien-l-01 surfaces are similar when protonation occurs at the oxygen atom. Both have minimum conformers with an orthogonal orientation of the hydrogens at oxygen. Furthermore, both PES’s for vinyloxonium and 1,3-butadienyloxonium cations are complex at the STO3G basis level, and both surfaces are simplified at the 3-21G basis level. When protonation occurs a! to the oxygen atom, the protonated 1,3-butadien-l-01 cations behave significantly differently to those of protonated vinyl alcohol. Firstly, the 1-hydroxy-lH-1,3-butadienium cation does not collapse to a three-membered ring as does the 2-hydroxyethenium cation. Instead the 1-hydroxy-lH-1,3-butadienium cation is stabilized by firstly an allylic cation formation, and secondly by a pseudo six-membered ring isomer (4-2-5) when the (CCCC ) is in a Fyn configuration. The final noteworthy feature on the protonated 1,3-butadien-l-01 surface is that when protonation occurs at the carbon y to the oxygen atom to form the 4-hydroxy-2H-1,3-butadienium cation, this cation collapses to stable threemembered rings when the (OCCC) is in a trans configuration and to both three- and five-membered rings with a cis (OCCC) configuration. The interesting feature about these rings is that as the basis set is improved, the stability of the rings, especially the five-membered ring, increases. Hence, the fivemembered rings, and possibly larger ring isomers, are in all likelihood real isomers on the PES’s. The major problem encountered in the investigation of the PES’s of the

protonated vinyl alcohol, methyl vinyl ether and 1,3-butadien-l-01 is that the surfaces are too flat with respect to rotamer barriers. This becomes more of a problem as the length of the carbon chain is increased. The choice of basis sets for future work may exclude the STO-3G basis set because it overestimates the stability of small ring isomers and because of the problems associated with the oxygen protonated PES encountered in this study. Use of the 3-21G for geometry optimization should yield superior results over the STO-3G basis set and should reduce the computations required in future work. Improved relative energies can still be obtained with 6-31G* single point energy calculations on optimized 3-21G geometries. The results in Table 6, which compare the various basis sets at the Hartree-Fock and Moller-Plesset theory levels, reveal that the higher level calculations (i.e. MP2 and MP3) incorporating electron correlation are not as important as Nobes and Radom [ 241 claim them to be in providing an accurate description of the protonated methyl vinyl ether PES. This is because the relative energy differences between conformers are not as good as those determined using the HF/6-31G* energies. ACKNOWLEDGEMENTS

The continued financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged, as are useful discussions with Dr. M.R. Peterson.

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